Measuring the Universe: the Cosmological Distance Ladder

The early rungs of the distance ladder — distance scales on Earth, in the solar system, and to the nearest stars and galaxies — are well established. My book serves as a solid grounding for understanding these early rungs.

But science always progresses. This blog lets me discuss some of the newer distance-measuring techniques not in the book – such as the use of baryon acoustic oscillations as a standard ruler.

Back when I wrote Measuring the Universe, the most distant object then known had a measured redshift, z, of 5.64. That particular distance record was broken while the book was still in press, and since then numerous objects – primarily galaxies, but also quasars and gamma-ray bursts – have been detected at z > 5.64.

Today, the record holder for “most distant object” changed hands once again. Astsronomers using NASA’s Hubble Space Telescope measured the redshift of the galaxy GN-z11 to be 11.09. This is a HUGE redshift. It corresponds to an age of about 13.4 billion years. In other words, we are seeing the object as it was just 400 million years after the Big Bang!

As galaxies go, GN-z11 is quite small: about 25 times smaller than our own Galaxy and with only 1% of our Galaxy’s mass in stars. Nevertheless, it is surprising that a galaxy as large as this could form so soon after the Big Bang. Presumably we will learn more about the conditions that gave rise to these early galaxies as astronomers push the distance record back to z = 12 and beyond. Exciting times!

The inset in this field of galaxies shows GN-z11, the farthest galaxy ever seen (to date). We see the galaxy as it appeared 13.4 billion years in the past. The expansion of the universe has shifted the light from the GN-z11’s young, blue stars to the red.(Credit: NASA, ESA, P. Oesch, G. Brammer, P. van Dokkum, and G. Illingworth)

It’s not often that you come across a new method of distance determination in astronomy, but today’s Naturecontains a paper (“A dust-parallax distance of 19 megaparsecs to the supermassive black hole in NGC 4151” by Sebastian Hönig, Darach Watson, Makoto Kishimoto and Jens Hjorth) that describes a method for directly determining the distances to quasars and galaxies with active nuclei.

As I’m sure you’re aware, over the course of many decades astronomers have developed a “cosmological distance ladder”. If astronomers understand an object – how bright it really is, how big it really is – they can determine its distance by measuring how bright or how big it appears. However, each time astronomers step up one rung on the distance ladder they introduce a source of error. It’s inevitable. A much better way of measuring distance is to use a direct method: to use geometry, in other words.

The most familiar example in astronomy of distance determination through geometry is that of annual parallax. As Earth moves around the Sun, the position of a nearby star is seen to shift relative to the background of the more distant, “fixed” stars. Draw lines between Earth, Sun and star and we generate a huge triangle. But we can measure the angular shift, and we know the diameter of Earth’s orbit, so we have all the information we need to solve the triangle. (Assuming we’ve done basic geometry in school.)

Earth, Sun and star form a triangle. We know the base of the triangle and we can measure the parallactic shift caused by Earth’s motion. We can solve the triangle and determine the star’s distance.

If a star moves by 1 second of arc then by definition it would be at a distance of one parsec. All stars (except the Sun, of course) are further away than 1pc and so all angular shifts exhibited by stars are less than 1 second of arc. Indeed, although this method formed one of the earliest and most important rungs in the cosmological distance ladder, it is difficult to apply it to very distant objects because the angles involved are simply too small to measure.

How, then, can Hönig and his colleagues apply a geometrical technique to a galaxy that lies 19 million parsecs away? Aren’t the angles way too small to measure?

Well, these astronomers have “inverted” the familiar parallax triangle. The base of the triangle isn’t the diameter of Earth’s orbit, it’s size of a region surrounding an active galactic nucleus (in this particular case, it’s the size of a dust region surrounding the supermassive black hole in the nucleus of the galaxy NGC 4151).

The Seyfert galaxy NGC 4151 lies 62 million light years from Earth. In this image, blue is from X-ray observations; yellow dots are from optical observations; and red is from radio observations. (Credit: NASA, ESA)

In order to solve the triangle formed by Earth, the supermassive black hole in NGC 4151, and the dust region surrounding the black hole, astronomers need to measure two things: (i) the base of the triangle – in other words, the true distance between the black hole and the dust, and (ii) the smallest angle in the triangle – in other words, angular size of the dust cloud.

The distance between the black hole and the dust cloud is easy to measure in principle – though difficult and messy in practice. As matter falls towards the black hole it heats up, so infalling matter produces radiation from a region just outside the event horizon. (Note that, although the black hole has a huge mass the radius of the event horizon is small. This is not a big object.) The radiation spits, and flickers, and flares: it’s highly variable. So suppose there’s a flash of light from just outside the event horizon. Some of the light will take a path directly towards our telescopes; some of the light will head of at right angles and continue until it interacts with dust clouds. This interaction will cause the dust to light up (or “reverberate”), which our telescopes will detect some time after the detection of the initial flash. By measuring the time delay astronomers can thus calculate the length of the base of the triangle (it’s just the delay multiplied by the speed of light). The technique is called “reverberation mapping”.

The angular size of the hot dust clouds that surround active galactic nuclei can be determined with a sufficiently precise interferometer. The Keck interferometer has sufficient resolution to measure the angular size the dust clouds in NGC 4151, and this is what Hönig and his colleagues did. By using the angular size determined by the Keck interferometer with lengths determined by a previous reverberation mapping project they were able to solve the NGC 4151 triangle: it’s 19 Mpc away (give or take 2.5 Mpc).

This distance comes from geometry. There’s no chain of inference involved as there is with the cosmological distance ladder: geometry gets you there directly.

The method has great potential because active galactic nuclei are bright enough to shine all the way across the universe. If we were to develop interferometers with increased resolving power (rather than just developing telescopes with ever-greater light-collecting ability) then we would have the ability to use geometry to measure distances over cosmological scales.

One of the distance-measuring techniques I described in Measuring the Universe was that of main sequence fitting. It’s a method for deriving the distance to an open star cluster. The idea is that you lay a plot of the HR diagram of the distance cluster on top of the HR diagram for a nearby cluster at a known distance (such as the Hyades). By comparing the brightness you can estimate the distance. Simple.

The problem with this method is that the Hyades is quite an old cluster of stars; we can use it to calibrate the lower part of the main sequence but not the upper part, where bright young stars reside. That’s where the Pleiades come in useful. It’s a much younger cluster, with some luminous stars. (The Pleiades is often known as the Seven Sisters, because of seven bright stars that are visible to the naked eye, but the cluster contains many more stars: Galileo counted 36 stars with his first crude telescope, and we now know that the cluster contains more than a thousand stars.) So if we know the distance to the Pleiades then we can be confident in using main sequence fitting as a tool for measuring distance. The Pleiades thus provides an important rung of the cosmological distance ladder.

A Hubble image of the Pleiades star cluster (Credit: NASA/ESA/Caltech)

The problem is that astronomers are not particularly confident about the distance to the Pleiades.

Before I began my research for Measuring the Universe, the commonly accepted distance to the Pleiades was about 134 parsecs; a variety of independent techniques and measurements arrived at that answer. More recent measurements using the Hubble Space Telescope suggest a distance of 135 to 140 parsecs. While I was writing Measuring the Universe, however, results from the Hipparcos astrometry mission produced a Pleiades distance of just under 120 parsecs – a significantly smaller distance. Since the Hipparcos scientists obtained their distances from parallax observations – which rely just on geometry, and thus should be reliable – one can’t easily dismiss their findings. So how far away is the Pleiades cluster? About 120 parsecs distant? Or 135–140 parsecs distant? It’s an important question.

In a recent paper (“A VLBI resolution of the Pleiades distance controversy“), Carl Melis and colleagues describe their own parallax-based measurements of the Pleiades distance. They used very long baseline radio interferometry to determine an absolute distance to five stars in the cluster. Their result? They obtain a distance of 136 ± 1.2 parsecs, which is consistent with all those other measurements. Their result seems to consolidate this particular rung of the distance ladder – but it does raise a question: why did Hipparcos produce a distance that was about 12% too small?

Close your left eye and align your upright index finger against some distant object. Then open your left eye and close your right eye. Your finger has moved, relative to the background object. This is the phenomenon known as parallax, and it arises whenever you look at an object from two spatially separated vantage points.

The importance of parallax is that it enables you to calculate distances. Since you know the distance between your eyes, and you can measure the angle through which the object has appeared to move, the application of some simple trigonometry gives the distance to your finger. Of course, figuring out the distance from your eyes to your finger isn’t a big deal – but precisely the same logic allows you to figure out the distance to nearby stars.

The Earth moves around the Sun, so when we look at a nearby star in January and in July we look at it from different vantage points: the nearby star appears to move relative to the background of the distant “fixed” stars. In other words, the nearby stars exhibit a so-called annual parallax. Since we know the distance between Earth and Sun (this is one of the earliest rungs on the cosmological distance ladder) and we can measure the angle through which the star appears to move over the course of a year, the application of some simple trigonometry gives us the distance to the star.

As Earth makes its yearly orbit of the Sun, a nearby star is seen to make a tiny ellipse (relative to the distant “fixed” stars).

In Measuring the Universe I devoted a lot of space to a discussion of parallax, since it was the first technique that enabled astronomers to obtain accurate distances to nearby stars – the first successful measurement of an annual stellar parallax was made by Bessel in 1838 for the star 61 Cygni. However, there’s a difficulty in trying to use parallax as method of distance measurement in astronomy: the angles involved are so tiny. Even the nearest star has an annual parallax of less than 1 second of arc. (The parsec is defined as the the distance at which an object will possess an annual parallax of 1 second of arc; it corresponds to 3.26 light years. The Centauri system, of course, is 4.37 light years distant.) As time goes by, however, the accuracy with which astronomers can make measurements increases. Indeed, the other reason I spent so long discussing parallax was that, during the writing of the book, the results of the Hipparcos mission were being disseminated – Hipparcos (“High precision parallax collecting satellite”) represented a step-change in the field of astrometry.

Hipparcos was an ESA mission, which was launched in 1989 and ran until 1993. It was the first space experiment devoted to astrometry – the accurate measurement of the position of stars. The final Hipparcos Catalogue contained information on the parallaxes of about 120,000 stars – with a median accuracy of better than 0.001 seconds of arc.

In Measuring the Universe I wrote that ESA were hoping to develop a successor mission to Hipparcos. The planned mission, called Gaia, would map not 100,000 stars but a billion stars. And the positional accuracy would not be measured in milliarcseconds but in microarcseconds (20 microarcseconds at a stellar magnitude of 15, and 200 microarcseconds at a magnitude of 20). Gaia would measure the distances of 20 million stars to a precision of 1%, and of 200 million stars to better than 10%. Such a mission would inevitably impact on many other fields (such as extrasolar planet determination, the testing of general relativity, quasar discovery…)

When I wrote the book, the Gaia mission was so far in the future that I found it difficult to imagine that it would ever fly; I thought it would be lost in the maze of technological, computational and political obstacles that were in its way. But Gaia is on its way! It launched successfully today, 19 December 2013, at 09:12GMT and in a month or so it will be at its new home at the Earth-Sun L2 point.

The plan is for Gaia to observe the sky for five years; astronomers will be analysing the Gaia data for much longer than that. This new astrometric mission is going to have a huge impact on all aspects of astronomy.

Measuring the distance to celestial objects is probably the most difficult problem in astronomy: unless you know the intrinsic brightness or size of an object, you can’t tell its distance simply by measuring its apparent brightness or size. A large, bright, distant galaxy looks the same as a small, dim, nearby galaxy. Conversely, if we know the distance to an object then we can begin to understand many of its most important physical characteristics, such as its size and luminosity.

As I explain at length in Measuring the Universe, astronomers estimate how far away something is by making use of the so-called cosmological distance ladder. The idea is that by understanding the behaviour of objects that are nearby we can estimate distances to objects that are further away; by understanding behaviour on that larger distance scale we can reach out and estimate distances to objects that are even further away; and so on. We start by determining the radius of the Earth; that gives us a clue to the scale of the solar system; that in turn gives us a clue, via parallax, to the distance to the nearby stars; by understanding the nature of stars we can estimate the size of the Galaxy; and so on and so on, until we can determine the size of the Universe by determining the Hubble constant H0.

The problem with this approach is that an error in one of the early rungs of the distance ladder will propagate through to the later rungs: when astronomers in the last century corrected their misunderstanding of the brightness of a type of variable star called a Cepheid, their estimate of the size of the Universe doubled.

Establishing the distance to the Large Magellanic Cloud (LMC), one of the closest galaxies to our own, provides the basis for one of the early rungs on the cosmological distance ladder. If we have an accurate determination of the LMC distance then we can calibrate various distance-measuring techniques that in turn let us measure objects at cosmological distances. In Measuring the Universe I gave the results of three distance estimates to the LMC. Cepheid measurements produced a distance of 50 kpc; a technique based on measuring the tip of the red giant branch yielded a distance of 48 kpc; and RR Lyrae stars gave a distance of 45 kpc. Each technique had its associated errors, of course, but there was a 10% difference between the Cepheid and the RR Lyrae methods. It would be good to measure the LMC distance with more accuracy.

Well, this week’s Nature contains a paper entitled “An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent“. Grzegorz Pietrzyński and his colleagues observed eight binary systems over a period of almost ten years. These eight systems were “eclipsing” binaries: in other words, because of the orientation of their orbits with respect to Earth, our telescopes observe them to pass in front of each other. As one star eclipses another, the total brightness of the pair diminishes; and it diminishes by different amounts depending on which star is doing the eclipsing. By making careful observations of these changes in brightness, and combining them with measurements of the orbital speeds of the stars, the Pietrzyński team were able to estimate the distance to the LMC: it’s 49.91 ± 0.19 kpc away. (There is a systematic error of 1.11 kpc.)

How the apparent brightness of an eclipsing binary system changes with time (Credit: NASA)

The eclipsing-binary measurement agrees well with the latest LMC distances using other techniques. Astronomers are firming up one of the key rungs of the distance ladder.

Well that didn’t last long. Last week I blogged about the discovery of a new most distant galaxy, and explained how in the years since the publication of Measuring the Universe the redshift of the most distant known object had been pushed back from 5.64 to about 11. A few days later and astronomers announce that the new record holder is at a redshift of 11.9!

The new result comes from UDF12, the Ultra Deep Field 2012, a survey program that points Hubble at a tiny patch of sky (just one-tenth the diameter of the full Moon) in the constellation Fornax. The aim is to take the deepest ever image of the heavens. Astronomers on UDF12 use Hubble’s Wide Field Camera 3 to take infrared pictures with huge exposure times. Very gradually, they build up images of incredibly distant objects. And one of the objects they imaged, UDFj-39546284, has a redshift zof about 11.9: the light that Hubble detects now set off from the galaxy when the Universe was just 380 million years old.

The Hubble Ultra Deep Field, with the redshifts and positions of seven galaxies indicated. The UDF12 program suggests that one of these galaxies has a redshift of 11.9 – the most distant object yet seen.(Credit: NASA/ESA/R. Ellis/Hubble UDF12 project)

Perhaps the most interesting aspect of this work is that the stars already contain heavy elements, which must have originated in the nuclear reactions taking place in an earlier generation of stars. Even at these redshifts we still haven’t seen the first generation of stars.

When I wrote Measuring the Universe, the most distant galaxy that astronomers had ever observed lay at a redshift of z = 5.64. In the intervening years, the record for “most distant galaxy” has never been held by one object for long; astronomers keep peering further back in time and further out in space. The latest object to hold the record is MACS0647-JD, a tiny galaxy that lies at a redshift of 11 (give or take).

The galaxy’s discovery is described in a recent preprint (15 November 2012) entitled CLASH: Three Strongly Lensed Images of a Candidate z ~ 11 Galaxy. CLASH stands for Cluster Lensing And Supernova Survey with Hubble (yes, it’s yet another acronym): it’s an international group led by Marc Postman of STSI that uses the gravitational lensing effect of massive galaxy clusters to magnify distant galaxies that lie behind them. In the case of MACS0647-JD, light from this ancient galaxy set off on its way to us about 13.3 billion years ago. About 8 billion years after it set off on its journey, the light encountered a galaxy cluster called MACS J0647+7015. This cluster is so massive that it distorts the spacetime around it, causing light from MACS0647-JD to take multiple paths. The CLASH team were able to observe three different, magnified images of the galaxy; without the gravitational lens provided by nature it would have been extremely difficult to observe such a faint, distant object with current telescopes.

MACS0647-JD is so far away, in fact, that it might be a long time before for a telescope confirms the redshift based on spectroscopy. But the CLASH analysis looks robust: this tiny object, just 600 light years in diameter, is the current galactic distance record holder.

A composite image of MACS0647-JD taken by instruments on the Hubble Space Telescope. The inset shows a close-up of the galaxy.(Credit: NASA, ESA, M. Postman & D. Coe (STScI), & CLASH Team.)

In Measuring the Universe I talked about the Sunyaev-Zel’dovich effect (or the SZ effect, for short). It’s named after Rashid Sunyaev and Yakov Zel’dovich, who studied the concept in the late 1960s and early 1970s.

The SZ effect is a distortion in the observed cosmic microwave background radiation caused by high-energy electrons scattering of low-energy CMB photons. The collisions give the photons an energy boost – it’s the familiar inverse Compton scattering effect – and this in turn generates a slightly hotter patch in the microwave background. (‘Slightly’ is the operative word here: a microwave photon passing through a cloud of hot electrons on its journey towards Earth will appear hotter by just a few millionths of a degree.)

The high-energy electrons that can cause the SZ effect are to be found in the extremely hot gas clouds that are found at the centre of galaxy clusters. And, because the SZ effect is caused by scattering, its size doesn’t depend on redshift. In other words, the SZ effect in a high-redshift cluster can be detected just as easily (or, more truthfully, with just as much difficulty!) as in a cluster at low redshift. The SZ effect provides what is in essence a standard ruler – see Measuring the Universe for details – and so it can be used as a distance indicator over quite large reaches of the cosmos.

But there’s another type of SZ effect – the so-called kinematic SZ effect. I didn’t bother discussing it in the book because it is about 20 times fainter than the main (or thermal) SZ effect. Since the thermal SZ effect is hard enough to measure I didn’t think that anyone would be measuring the kinematic SZ effect anytime soon. Well, I was wrong. Cosmologists have now measured it.

The kinematic SZ effect arises because of the motion of galaxy clusters. Imagine a CMB photon passing through a cluster that’s moving away from us: when we observe the photon it will be slightly cooler (redder) than it otherwise would be due to the kinematic SZ effect. And if the photon moves through a cluster that’s approaching us then it will be slightly hotter (bluer). Sunyaev and Zel’dovich considered this from a theoretical point of view four decades ago, in 1972; but it’s taken until 2012 for researchers to measure it, such is the difficulty of teasing out the signal.

If a CMB photon passes through a galaxy cluster that’s moving away from Earth it becomes slightly redder and cooler (left part of the diagram). If it passes through a galaxy cluster that’s moving towards Earth then it becomes bluer and hotter (right part of the diagram). These wavelength shifts are extremely tiny, so this effect has only just been observed. (Credit: Sudeep Das, University of California-Berkeley)

The SZ effects can probe how clusters form and move around – something that depends critically on dark matter and dark energy. The SZ effects thus have the potential to deepen our understanding of the most mysterious elements of our Universe.

There’s an interesting paper in the 6 June 2012 issue of Phys. Rev. Letters. The paper, entitled “Using quasars as standard clocks for measuring cosmological redshift” (and available as a preprint here on arXiv) describes how quasars might be used to probe the largest distances in the Universe.

The use of standard candles has of course been important in developing an understanding of the distance scale of the Universe. If you know how bright something really is, then by measuring how bright it appears you can determine its distance. In essence, you just have to employ the inverse-square law.

A standard candle appears dimmer the more distant it isCredit: Karen Kwitter

Cepheid variables, for example, were used to probe the local Universe; type Ia supernovae have allowed astronomers to probe even deeper into the cosmos. However, to probe the largest distances with a standard candle we need the brightest sources. The most distant known supernova occurred at a redshift of 1.7; to get beyond that we need to use something like quasars (which have been identified at redshifts beyond 7). The trouble with quasars, however, is that they vary hugely in luminosity. They certainly aren’t a standard candle.

But could quasars be a standard clock?

Dejan Stojkovic and his colleagues have analysed the light curve data of 13 quasars, each of which was at a different redshift. They plotted a graph of quasar flux (in other words the actual energy emitted per unit time) against time. All values were transformed into the rest frame of the quasar, so in each case the light curve described what was happening when the radiation was emitted. When they laid the different light curves on top of one another they found that the curves matched. That leads to an intriguing thought: if quasar light curves are similar then you can use the redshift of one quasar to determine the redshift of an unknown quasar simply by recording how its brightness changes over time. Stojkovic and his colleagues tested two methods for doing this.

First, they identified straight-line segments in the light curves that were related to quasar redshift and then discarded the rest of the light curve. They then matched the slope of this straight line for a quasar with known redshift to the slope of a line from the light curve of an “unknown” quasar (whose redshift they of course knew). The method gave accurate values for the unknown resift.

Second, they employed a more statistical approach that matched several parts of the quasar light curves (rather than just a straight-line segment). Again, by fitting a “test quasar” light curve to an “unknown quasar” light curve, they were able to find the ratio of the redshifts with good accuracy.

Thus if Stojkovic and colleagues are correct then astronomers might be able to use quasars as standard clocks. It’s potentially a new technique for determining cosmic distances. It isn’t going to be instantly useful: they need to check the technique on more than just 13 quasars, and they need to develop algorithms to do the light-curve matching. It would also help if we knew why such a relationship exists: at present the authors have no theoretical explanation for the effect. But if the work stands up, astronomers will soon have a tool that lets them probe distances on a truly cosmological scale.

Standard candles have played a hugely important role in establishing the cosmological distance ladder. It’s easy to see why: the more distant something is the dimmer it appears, according to the inverse-square law. So if we know how bright something really is then, by measuring how bright it appears to be, we can determine its distance.

A standard candle appears dimmer the more distant it is Credit: Karen Kwitter

Cepheid variables and Type Ia supernovae are perhaps the most well-known standard candles, and the study of these objects have transformed our understanding of the universe. But they (and the several other standard candles used in astronomy) are not without problems. One of the main difficulties is that we can’t see them over very large distances. Even Type Ia supernovae cannot be used to make reliable distance measurements beyond a redshift of about 1.7. So one of the most interesting astronomical results of 2011, at least in my opinion, was the surprising discovery of a standard candle that can work over truly cosmological distance scales: active galactic nuclei (AGNs).

An artist's impression of an accretion disc and torus around an AGN Credit: NASA/CXC/M.Weiss

An AGN is one of the brightest objects in the universe and so can be seen over extreme distances. The power source for an AGN’s extreme luminosity is the supermassive black hole that lies at its centre. An accretion disc – a collection of matter that forms as matter spirals into a dense object – surrounds an AGN’s supermassive black hole. (See chapter 4 of New Eyes on the Universe for an explanation of accretion discs.) Further away from the black hole, at least with type-1 AGNs, lies a dense area of dust and gas known as the broad-line region. The region gets its name because the black hole’s gravitational influence whips the dust and gas around at high speed, and the Doppler effect causes emission lines to be broadened.

And how does this rather chaotic set-up generate a standard candle? Well, the broad-line region emits light because its gas has been ionised. The ionisation occurs because high-energy photons are emitted by the accretion disc and subsequently hit the region. The key point here is an accretion disc is a variable object: sometimes it ‘flares’. This makes it possible to compare the time at which the accretion disc emits light and the broad-line region re-emits light, and that time delay gives the radius of the broad-line region. What four astronomers – Darach Watson, Kelly Denney, Marianne Vestergaard and Tamara Davis – have found is that there’s a relationship between the size of the radius and the central luminosity of the AGN. They checked the relationship on a sample of 38 AGNs at a known distance and it seems that, although there is scatter in the data, the technique will work as a distance indicator. (You can read their paper at arxiv.)

The AGN standard candle is not as accurate as the Cepheid or supernova candles. But since AGNs can be seen over tremendous distances, and since they can be studied over long periods of time, it seems certain that the technique will become of increasing importance. In particular, a standard candle that lets astronomers measure distances directly up to a redshift of about 4 will provide a valuable tool for probing the nature of dark energy.